Transcript me.lsu.edu

MATLAB Tutorials
Session I
Introduction to MATLAB
Rajeev Madazhy
Email: [email protected]
Dept of Mechanical Engineering
LSU
Tutorial Outline
Session 1: Introduction to MATLAB
Session 2: Programming in MATLAB
Session 3: Plotting in MATLAB
Session 4: Mathematical Applications using MATLAB
Session 5: Mathematical Applications using MATLAB (cont.)
Session 6: Engineering Applications using MATLAB
Session 7: Open for specific problems
Department of Mechanical Engineering, LSU
Session Outline






Overview of MATLAB
Using the built-in functions
Constants and Variables
Basic Arithmetic Operations
Matrices and Computation
Solving simple equations
Department of Mechanical Engineering, LSU
What is MATLAB?
MATLAB is basically a computing tool for engineers and
mathematicians.
Features include:
 Interactive programming environment
 Graphing facilities
 Built-in functions
 Toolboxes designed for specialized field of applications
Department of Mechanical Engineering, LSU
Background info about MATLAB

MATLAB is an acronym for Matrix Laboratory

Cleve Moler was the original creator of MATLAB

MATLAB is now a product of Math Works Inc. cofounded by Cleve Moler and Jack Little.

First version of it appeared as early as 1981

Initially written for matrix computations, it contained
only 3000 lines of source code written in FORTRAN
Department of Mechanical Engineering, LSU
What can MATLAB do for you?
 Produce effective solutions
 Compact the time invested in analysis and development
 Reduce project costs
 Quickly test and compare multiple alternatives
 Modeling and simulation
 ……………………………………………….ad infinitum
Department of Mechanical Engineering, LSU
Getting Started…….
Prerequisites:
 Basic knowledge of linear algebra
 Some computer experience (helpful but not necessary)
 Curiosity!!!!!
Department of Mechanical Engineering, LSU
Basic Arithmetic Operations
Addition
:
a+b
Subtraction
:
a- b
Multiplication
:
a*b
Division
:
a/b
Power
:
a^b
Note the symbols being used for the operators.
Department of Mechanical Engineering, LSU
In MATLAB….
Department of Mechanical Engineering, LSU
Naming Constants and Variables
 The value of  is stored in MATLAB as pi
 The contents of the variable ans change with every answer
 Variable names can contain upto 31 characters
 Every variable must start off with a letter
 When you write the semicolon ‘;’ at the end of the statement
the computer will not display the result after you press the
return key.
 MATLAB is case sensitive. A & a are identified different
Department of Mechanical Engineering, LSU
In MATLAB….
Department of Mechanical Engineering, LSU
Built-in math functions
abs(x)
absolute value of x
Sin(x)
sine of x (where x is in radians)
asin(x)
arcsine of x
exp(x)
exponential of x
log(x)
natural logarithm of x
log10(x)
base 10 logarithm of x
sqrt(x)
square root of x
imag(x)
imaginary part of complex number x
real(x)
real part of the complex number x
Department of Mechanical Engineering, LSU
In MATLAB…..
To get more information about other functions type at command prompt:
>>help elfun
Department of Mechanical Engineering, LSU
Vectors and matrices

An ordered collection of numbers separated by commas or
spaces can be defined in MATLAB as an array or vector

Example: A=[1 2 3 4 5] is an array of 1 row and 5 columns

A matrix is defined as an array of n  n elements

The elements of an array are identified by their index

The number of elements of an array can be retrieved using
the length function

The addition and subtraction are defined only for arrays of
the same length
Department of Mechanical Engineering, LSU
In MATLAB….
Department of Mechanical Engineering, LSU
Vectors and matrices (cont..)

Array of equally spaced elements can be entered by stating
the first element, the increment and the last element

When the increment is 1 it can be omitted
Department of Mechanical Engineering, LSU
Vectors and matrices (cont..)

Array multiplication in MATLAB is indicated by “.*”

For example : A.*B is the product of two arrays

Array division in MATLAB is indicated by “./”

For example : A./B is the quotient of two arrays

We can also raise the elements of the array to the same
power by using the operator “.^”

Many built-in functions can be applied to the array by
simply using the array name as the argument
Department of Mechanical Engineering, LSU
In MATLAB….
Department of Mechanical Engineering, LSU
Simple plots using arrays
Department of Mechanical Engineering, LSU
Plot result…..
Department of Mechanical Engineering, LSU
Row Vectors and Column Vectors
 One dimensional arrays can be considered as row vectors
 Column vectors are generated by entering an array of
numbers separated by semicolons “;”
 Row vectors and column vectors can be converted into each
other by transposition operation “ ‘ “
Department of Mechanical Engineering, LSU
In MATLAB….
Department of Mechanical Engineering, LSU
Defining a matrix
 Matrices are defined as two dimensional arrays
 Different rows are separated by semi colons or type
each row separately and press enter
 Any element of a matrix is identified by two indices:
the first indicates the row and the second indicates
the column
Department of Mechanical Engineering, LSU
In MATLAB….
Department of Mechanical Engineering, LSU
Cont…
 The number of rows and columns in a matrix is retrieved by
size function
 We can create a new matrix by putting two matrices besides
each other
Department of Mechanical Engineering, LSU
Cont…
 We can also extract a sub matrix out of a matrix
Department of Mechanical Engineering, LSU
Cont…
 We can generate a matrix with the same number of rows and
columns as A, with all the elements equal to one, using the
command ones
 Similarly using the command zeroes we can get all the
elements of the matrix as zeroes
Department of Mechanical Engineering, LSU
Polynomials….

Polynomial x 2  2 x  4 is expressed in MATLAB as an array of
coefficients, A=[1 2 -4]

The equation is solved by using the function roots(A)

The coefficients of the polynomial can be retrieved from its roots
through the function poly()

The value of a polynomial at point x is obtained by function
polyval(A,x) where A is the array, the coefficients of the
polynomial are stored
Department of Mechanical Engineering, LSU
In MATLAB….
Department of Mechanical Engineering, LSU
Complex Numbers
Department of Mechanical Engineering, LSU
Solving systems of Equations…
x1+ 2x2 + x3 = 4
2x1+ 3x2- x3 = 9
4x1- x2 +2x3= 0
1 2 1 
A  2 3  1
4  1 2 
A X  B
Department of Mechanical Engineering, LSU
 4
B  9 
6
X  A1  B
In MATLAB….
Department of Mechanical Engineering, LSU
Looking ahead….
There are several books written on MATLAB where a good
Description about the functions is given.
 Introduction to MATLAB for Engineers and Scientists
Delores M. Etter & David C. Kentucky
 A guide to MATLAB: for Beginners and experienced users
Brian R. Hunt, Ronald L. Lipsman & JM Rosenberg
Department of Mechanical Engineering, LSU
Next Session….
Programming in MATLAB :
 How to use M Files
 Programming functions
 Control Structures
 Displaying output in different formats
Department of Mechanical Engineering, LSU
Thank You
Department of Mechanical Engineering, LSU